Ground-State Wave Function of Shallow Donors in Uniaxially Stressed Silicon: Piezohyperfine Constants Determined by Electron-Nuclear Double Resonance

Abstract

Stress-induced changes in the ENDOR spectra of a shallow donor electron interacting with various ${\mathrm{Si}}^{29}$ nuclei neighboring the donor have been experimentally and theoretically investigated. For each of the three measured donors - As, P, and Sb - the compressional, uniaxial stress was applied along the [001] axis and its magnitude corresponded to strains up to ${10}^{-3\mathrm{}}$. To describe the observed linear and quadratic shifts and splittings of the lines in an ENDOR shell, we have defined a set of piezohyperfine constants. One piezohyperfine constant was measured for each $〈111〉$-axis-class shell; three independent piezohyperfine constants were measured for each shell of the other shell symmetry classes. Piezohyperfine constants are reported for more than 15 measured lattice shells about each donor. Analysis of the results shows that the constants for any one shell can be attributed primarily to changes in the Fermi contact hyperfine constants at the various lattice sites within that shell. Consequently, the stress-induced changes are directly related to wave-function density changes at specific points in the lattice. Calculations of these wave-function density changes have been performed using a model based on the valley-repopulation effect and on an effect due to the redistribution of the radial envelope function (RREF effect). The calculations and experimental results are qualitatively in good agreement. The quanitative theoretical accuracy is not sufficient to match all the experimental shells to the actual lattice shells, but a new match of shell $Q$ and the (1,1,5) shell has been determined and other matchings are suggested. The theoretical and experimental results provide information on two intrinsic lattice parameters: the deformation-potential constant ${\Xi }_u$, and the location of the conduction-band minimum $k_0$. Difficulties with assigning a value to ${\Xi }_u$ because of the RREF effect are discussed. A revised "spin-resonance" value for ${\Xi }_u$ was found to be 10 ± 1 eV. Applying the above model to the previously matched shells [A and (0,0,4), $B$ and (4,4,0), $K$ and (0,0,8)], one finds an average $k_0=(0.86\mathrm{}\pm 0.02)k_{max}$.